It's unclear as to why Apple has oddly continued this annoyance throughout iterations of iOS.
I've read it's a closure of backdoor security flaw.
Can you get around it?
Well, if you Google it, you'll most likely come across an Apple Forum discussion where a very bullheaded moderator pedantically type-slaps innocent question after innocent question.
The actual answer is "Yes and No."
First, you could tediously remove all your photos from albums and just organize them once synced in programs like iPhoto.
You can sync your iOS device over iCloud and view the photos in albums at any time. If you run over your limit of storage you may want to consider buying more storage. (If that organization is worth it to you.)
Finally, you can use "total access software "PhoneView" for the Mac by ecamm.com - this program allows access to all your photos.
Personally, I like the last option. I use "PhoneView" more than I use iTunes to manipulate files on my iPhone and even to create more space.